Acoustic Holographic Recording and Reproduction System Using Meta Material Layers

ABSTRACT

Holographic sound is recorded and reproduced by way of a single monaural recording per left and right ear recorded. This is accomplished by determining the phase shift of frequencies recorded after dividing the sound into discrete frequencies in a recording device having resonators, each resonating at a different frequency, placed in a circular arrangement and divided into discrete channels by non-resonant material. The resonators are placed in a pseudo-randomized arrangement within the recording device and the circle of resonators is in front of a microphone which records the sound monaurally. Playback is then by way of arranging speakers or transducers into micro perforated sheets which amplify the sound, the arrangement of speakers/transducers around a central point. The sound is then played back directionally based on the position where the sound originally was recorded from and the position of the particular transducer around the central point.

FIELD OF THE DISCLOSED TECHNOLOGY

The present disclosure relates generally to recoding and reproduction ofsound, and more specifically, to recording and reproduction of soundholographically.

BACKGROUND OF THE DISCLOSED TECHNOLOGY

Basic audio recording and reproduction technology is omnipresent and hasbecome an integral part of our daily life. These areas cover the fullsequence from recording to reproduction in, for example, music recordingin studios, concert halls, etc. and subsequent reproduction in homeentertainment systems, telephony/office communications, public addresssystems, etc. The ultimate goal is to reproduce sound exactly as itsounded when first created. In other words, we would like to be in thesame acoustic field in which it was originally recorded, in terms ofvarious factors, such as amplitude, frequency content and depthperception, spatial location, etc.

In recent times, steps have been taken towards virtual video/acousticrecording and reproduction in this area. Virtual acoustic recording andreproduction refer to the recording of real-world acousticconcerts/performances in reverberant spaces and their subsequentacceptable reproduction in a virtual version of the original performancespace, known as a Virtual Auditory Environment (VAE). Auditory scenescan be created using two main mechanisms: recording or auralization. Inthe first approach, recording for scene synthesis is usually implementedin a studio environment. For example, in popular music production, amulti-track approach is taken, whereby instruments are layeredtemporally, spectrally and spatially. Another example is in cinema,where Foley artists create the auditory scene by adding in everydaysounds synchronized to the actor's movements. In the second approach,the creation of auditory scenes through auralization involves theprocessing of recorded audio (preferably anechoic) with acousticresponses taken in real rooms or computed with auralization software.Unlike virtual reality, which takes us all the way to a new reality,holograms and holographic sound are those which creates some3-dimensional image in our “own reality”. Thus, holography andholographic sound is defined as a technique which enablesthree-dimensional sound processing by the brain (holograms) to becreated such that the brain detects a directional source of the soundand can determine different directions from which the sound emanates,despite, in embodiments of the disclosed technology, two soundsemanating from the same location in space. Accordingly, virtual realityis a reality which has been created via a computer. Augmented reality isvirtual reality but with bits added. Holography is a way of showing“pictures” (which includes an audio scene or “picture”) in which one canwalk around. Although virtual holographic video devices are now widelyavailable, virtual acoustic holographic recording and reproductiondevices are still primitive at the time of this writing.

Further describing holography, this is a technique to record andreconstruct the complete information of wave fields. The word‘holo-graph’ is derived from the Greek which means whole-drawing—whichalso describes the vast amount of information contained in a hologram.The basis of holography is spatial storage of the phase and/or amplitudeprofile of the desired wave-front, in a manner that allows thatwave-front to be reconstructed by interference when the hologram isilluminated with a suitable coherent source. Optical holograms have beenwidely applied in virtual reality displays, data storage, sensing, andsecurity printing.

Acoustic holograms, on the other hand, are relatively less advancedcompared to their electromagnetic counterparts in terms of presentapplications. One major restricting factor is the limited acousticproperties that natural or traditional materials can offer. Acousticholography is the process in which sound waves are recorded to tangiblemedium and arranged or reproduced in three dimensions using a processor.The sound field can be modeled to reconstruct its structure usingthree-dimensional (3D) images. The acoustic hologram could generate 3Dsound fields about 100 times more detailed than ones produced by othertechniques. To date, most acoustic holographic reconstruction techniquesrely on phased arrays with large numbers of active elements, requiringsophisticated phase shifting circuits, large power consumption andcareful calibration and tuning. Measuring techniques included inacoustic holography are becoming increasingly popular in various fields.The best-known techniques are based on Near-field Acoustic Holography(NAH). Nearfield-acoustic holography is a method for estimating thesound field near a source by measuring acoustic parameters away from thesource by means of an array of pressure and/or particle velocitytransducers. Near-field acoustic holography makes it possible toreconstruct the three-dimensional sound field between the source and themeasurement plane.

Holographic techniques are fundamental to applications such asvolumetric displays, high-density data storage and optical tweezers thatrequire spatial control of intricate optical or acoustic fields, withina three-dimensional volume. A variety of sound field reproductionmethods have been proposed such as Ambisonics, Wave Field Synthesis,methods based on the solution of an inverse problem and othertechniques. Recently, NAH (Near-field Acoustic Holography) has also beenconsidered for holographic systems. The major advantage of NAH is thatit enables reconstruction of all acoustic quantities such as theacoustic pressure, particle velocity and acoustic intensity not only ata measurement location, but in 3D space and on a source surface bymeasuring the acoustic pressure in the near-field of the target sourcesurface. NAH system includes a spherical array of a plurality ofmicrophones, an analog to digital converter for digitizing pressure datafrom each microphone, and a processor for determining the acousticintensity at each location, the processor having computer softwareadapted to apply a regularization filter to spherical Wave equations forpressure and velocity. Overall, NAH requires a large number of recordingand reproducing sensors—as large as 51 microphones and 51 speakers. Theneed for multiple transducers and system complexity are the majordisadvantages of the NAH approach. Furthermore, acoustical holography isstill limited by the Nyquist sampling theorem. To avoid spatial aliasingproblems, the array microphone spacing must be somewhat less than halfof the acoustic wavelength, which sets a serious limitation on the upperfrequency. Also, the resulting Nyquist rate is so high that a very highnumber of samples must be used. The combination of the large amount ofhardware (speakers, microphones) and large amount of processing makessuch systems cost prohibitive and difficult to implement.

Other simpler methods are limited to biaural sound. Sound is a vibrationthat propagates as an audible mechanical wave of pressure anddisplacement through a medium such as air and water. In human hearingterms, sound is the reception of such waves and their perception by thebrain. Many theorists earlier believed that only one ear was essentialfor correct hearing, but it has since been proven that two ears areessential for binaural hearing, and therefore, our understanding of theworld around us. In fact, the word “binaural” literally just means“using both ears.” The brain's hearing system is binaural, and thesemethods include relative phase shift for low frequency sounds, relativeintensity for sounds in the voice range, and relative time of arrivalfor sounds having fast rise times and high frequency components.Binaural recording is a method of recording sound that uses twomicrophones, arranged with the intent to create a 3-D stereo sensationfor the listener of actually “being in the room” with the performers orinstruments. Binaural sound is usually recorded with two microphonesspaced as if they were in place of your ears, sometimes actually in a“Kunstkopf” (dummy head), where the microphones are actually placedwhere your ear canals would be. The result, when using good headphonesfor playback, is a realistic sense of the space where the recording wasmade, and often an uncanny sense of the movement of instruments orvoices around that space, even sometimes seeming to come from above orbehind you. However, sound reproduction through headphones often leadsto ‘in-head localization’ such that good assessment of spatial cuesbecomes impossible.

On the other hand, normally mixed and panned multi-microphone studiorecordings intended for loudspeaker reproduction often use individualmicrophones on each instrument and are panned on the mixing console tosome location from far left to far right, with voices and often drumsplaced dead center, and other instruments moved left and right in theartificial image. When listened to such recordings using headphones, theimage often seems to be in the middle of your head rather than in theoriginal recording space. There have been various headphone and audioprocessor designs made to compensate for this “inside the head”perception over the years. It has been observed that while binauralrecordings sound their best on headphones, recordings mixed frommultiple tracks on studio loudspeakers usually sound their bestreproduced on loudspeakers.

Human hearing is three-dimensional. We can distinguish the directionand, to some degree, distance of a sound source. In fact, there's awealth of information in the sounds that reach our ears, and our brainsdo some very sophisticated processing of that information. The cochlea,and actually the whole ear, is designed to convert sounds into nervesignals and convey sound information to the brain. The cochlea of theinner ear is the most critical structure in the auditory pathway, for itis there that the energy from acoustically generated pressure waves istransformed into neural impulses. The cochlea not only amplifies soundwaves and converts them into neural signals, but it also acts as amechanical frequency analyzer, decomposing complex acoustical waveformsinto simpler elements. The human cochlea is capable of exceptional soundanalysis, in terms of both frequency and intensity. The cochlea allowsthe perception of sounds between 20 Hz and 20000 Hz (nearly 10 octaves),with a resolution of 1/230 octave (from 3 Hz at 1000 Hz). At 1000 Hz,the cochlea encodes acoustic pressures between 0 dB SPL (2×10⁻⁵ Pa) and120 dB SPL (20 Pa).

The cochlea is a hydro-mechanical frequency analyzer located in theinner ear. Its principal role is to perform a real-time spectraldecomposition of the acoustic signal in producing a spatial-frequencymap. The cochlea uses a frequency-to-space transformation to performaudio spectral analysis. Upon impingement of an acoustic signal onto thefluid-filled cochlea, the basilar membrane undergoes an oscillatorymotion at the frequency of the sound, resulting in a wave travelingtoward its distal end. The wave is spatially confined along the lengthof the basilar membrane, and the location of its maximum amplitude isrelated to the frequency of the sound. The higher the frequency, themore restricted the disturbance to the proximal end. Understanding offrequency analysis in the inner ear progressed through three mainperiods. The first was dominated by Helmholtz's suggestions that lightlydamped, spatially ordered, mechanically resonant elements in the cochleaperform the spectral analysis. The second period, lasting from the late1940s to the early 1970s was dominated by von Bekesy's description ofthe traveling wave. The third epoch during which a fundamentallydifferent paradigm has emerged. According to this paradigm, von Bekesy'straveling wave is boosted by a local electromechanical amplificationprocess in which one of the ear's sensory cell groups, outer hair cells,function as both sensors and mechanical feedback elements. Thisdiscovery helped to explain the cochlea's frequency selectivity. Thedifferences between Bekesy and Johnston's observations were due toactive biological mechanisms that act upon the vibration of the basilarmembrane in living subjects.

In the cochlea, the basilar membrane interacts with the fluid,constrained by the shape of the channel, to make a transmission linethat supports mechanical traveling waves. Positions along thistransmission line correspond to a large number of outputs, with aprogression of different frequency responses, analogous to the oldHelmholtz resonance view of cochlear function.

For a pure tone sound, active mechanics amplify basilar membranevibrations by around +50 dB at a very narrow section of the organ ofCorti, which serves to increase the sensitivity of the cochlea at thissite. Two similar frequencies can therefore activate two distinctcochlear regions, allowing them to be differentiated (a characteristicknown as frequency selectivity). This frequency tuning is closely linkedto the electro-motility of the outer hair cells (OHCs), and is definedby the fibers of the auditory nerve and the inner hair cells (IHCs) thatgenerate the neural signal.

One of the most significant nonlinear behaviors of the cochlea is highsound-level compression. Sound signals at low intensities are amplifiedin a frequency-selective manner at certain cochlear position, where thecochlea exhibits large gain, while high-level sound signals are barelyamplified, where the cochlea exhibits small gain. The auditory systemutilizes a unique method of real-time spectral decomposition along withplace theory to attain an impressive auditory range while maintainingreal-time processing capabilities. It is able to achieve this by actingas a hydro-mechanical frequency analyzer, as well as using compressivetechniques to efficiently transmit data. The inspiring functionality ofthe basilar membrane is its ability to perform real-time spectraldecomposition. Activation of sub-sections of the basilar membraneresults in sinusoidal vibrations of varying amplitude and phase,depending on the content of the input signal. Thus, in the inner ear atransformation takes place that maps frequency to location. Thismechanism is fundamental for the frequency discrimination of the ear.The location on the basilar membrane for maximal amplitude can bedescribed by:

$\left. {f = {{165.4\mspace{14mu} 10^{0.06x}\begin{matrix} \\

\end{matrix}} - 1}} \right)$${x = {\frac{1}{0.06}{\log \left( \frac{f + 165.4}{165.4} \right)}}},$

where:

f: frequency in [Hz]x: position of maximum excursion of the basilar membrane in [mm].

The frequency-dependent filtering mechanism of the human cochlea systemthus takes us to the spatial-frequency dependent design using dispersiveacoustic meta material (AMM) systems. As such, the basilar membrane hasoften been compared to a bank of band-pass filters (BPFs) thatsimultaneously decompose a convoluted signal into its frequencycomponents. A number of acousticians today think that the most realisticmodel of basilar membrane function is the resonator system, or, evenbetter, a system of frequency-tuned oscillators that can be regulated bythe central nervous system (known as efferent feedback).

Musical audio signals contain a large amount of underlying structure,due to the process through which music is generated. Human hearing isusually very good at analyzing the structure of audio signals, a processknown as auditory scene analysis. For music, it is not surprising that amusical audio signal would be generated from a small number of possiblenotes active at any one time, and hence allow a sparse representation.Compressed sensing (CS) seeks to represent a signal using a number oflinear, non-adaptive measurements. Usually the number of measurements ismuch lower than the number of samples needed if the signal is sampled atthe Nyquist rate. CS requires that the signal is sparse in some basis—inthe sense that it is a linear combination of a small number of basisfunctions—in order to correctly reconstruct the original signal.Clearly, the sinusoidally-modeled part of an audio signal is a sparsesignal, and it is thus natural to use CS to encode such a signals. Dueto its universality and lack of complexity on the sensor side, CS is anattractive compression scheme for multi-sensor systems. Recently,sparseness of audio signal has been exploited with the aim of achievingeven higher compression ratio than the current compression techniquesused in the multimedia coding standards.

It is known that an impedance-matched surface has the property thatincident wave generates no reflection. A perfect acoustic absorber ofdeep-subwavelength scale is of great scientific and engineeringinterest. It can act as the exact time-reversed counterpart of a pointsource, with important implications for time-reversal wave technology.Traditional means of acoustic absorption make use of porous and fibrousmaterials and gradient index materials, or employ perforated ormicro-perforated panels with tuned cavity depth behind the panels. Theygenerally result in either imperfect impedance matching to the incomingwave, or very bulky structures with dimensions comparable to thewavelength. Active ‘absorbers’, on the other hand, require costly andsophisticated electrical designs. Recently, it was shown that, forelectromagnetic waves, structuring the interface between two differentmaterials can lead to meta surfaces with diverse functionalities such asphase discontinuity, anomalous refraction/reflection, and polarizationmanipulation. Acoustic meta material based systems not only can recordwith fewer sensors but reproduce the sound with less speakers. Byexploiting acoustic meta materials and compressive sensing, aholographic recording device with fewer sensors that separatessimultaneous overlapping sounds from different sources and a speakerarray which can reproduce the holographic sound, a complete virtualacoustic holographic system is designed and presented. Anisotropicacoustic meta materials can be designed to have strong wave compressioneffect that renders direct amplification of pressure fields in metamaterials.

Thus, what is needed is a way to accurately reproduce holographic soundwhich is less expensive and better quality than what is currently knownin the art.

SUMMARY OF THE DISCLOSED TECHNOLOGY

A method of recording and reproducing sound holographically or in threedimensions, and devices to carry out same, are disclosed herein. Threedimensional sound recording and playback or holographic sound is definedas sound for which a healthy human brain can detect the direction fromwhich the sound emanated from, as well as differentiate from a directionfrom which another sound emanated from in any direction around a 360degree plane. This is accomplished in embodiments of the disclosedtechnology by receiving sound into a microphone after the sound has beenreflected and/or refracted off a plurality of resonators arranged intodiscrete channels. Resonators in embodiments of the disclosed technologyare acoustic resonators which vibrate and amplify a specific frequency.The “specific frequency” can be within 1 Hertz (Hz), 5 Hz, 10 Hz, or 20Hz depending on the embodiment. At the exact frequency of resonance, aspecific resonator will vibrate resonate most strongly compared to otherfrequencies.

The sound outputted by the microphone (that is, the sound waves receivedby the microphone which are produced by vibration of the resonators) isrecorded after applying a digital compression scheme to the sound. Thedigital compression scheme is described in the detailed description,below.

Based, at least in part, on a distance between each of the discretechannels to the microphone and a determined phase shift of at least somefrequencies within the sound (due to (known) distance from a respectiveresonator to the microphone), a plurality of piezo-drivers are vibrated.Piezo-drivers are devices which convert electrical impulses tomechanical impulses or vibrations. These piezo-drivers send vibrationsthrough acoustic metamaterial in a manner which at least partiallyrecreates directionality of the sound reflected or refracted off theplurality of resonators. The piezo-drivers and associated metamaterialis placed equidistant from a center point such that a direction of thesound can be reproduced by producing the sound in a correct directionaround the center point, though the shape of the device on which themetamaterial is arranged can be hexagonal, octagonal, and so forth (e.g.10, 12, 14, 16, sided).

The microphone used to record the sound can be monaural andomni-directional and calibrated to receive sound substantially equallyfrom each of the discrete channels. Each resonator resonates at adifferent frequency than each other resonator and are pseudo-randomlyarranged in a circular arrangement in front of a sound input end of themicrophone. In other words, the microphone is pointed in a firstdirection and the circular arrangement of the resonators is in front ofthe direction in which the microphone points, centered around, in someembodiments, an imaginary line extending from the tip of the microphoneoutwards past the front of the microphone. The pseudo-randomly arrangedresonators are arranged in discrete channels in a circular manner, thediscrete channels being separated from one another by non-resonantmaterial there-between each two channels of the discrete channels. Inother words, the resonators between each layer of non-resonant materialmake up a single channel. There is, around a circular or regularpolygonally cross-sectioned shape, an alternation between resonators andnon-resonant material with a plurality of resonators each designed toresonate at a different frequency, between each layer of non-resonantmaterial.

In embodiments of the disclosed technology, based on the distancebetween each discrete channel and the microphone as well as thedetermined phase shift, a direction from which the sound emanated isdetermined. This determination is then used to cause the plurality ofpiezo-drivers to vibrate the acoustic metamaterial. The correctpiezo-driver, based on it's position around the output/playback deviceis vibrated as a result so that the sound is outputted in the correctorientation in three dimensional space. It should be understood thatthis can also occur with the sound being emanated from multiplepiezo-drivers though the volume (as a result of amplitude of vibrationof the piezo-driver) of each will then correspond to the volume fromeach direction where the sound emanated. Likewise, when the soundemanated from a location in three dimensional space between two theposition of two metamaterial plates used for output, then each can bevibrated a lesser amount to recreate the sound from a direction betweenand so forth.

The plurality of piezo-drivers are equi-spaced around a center point ona sound reproduction device in manner lacking correspondence withplacement of the plurality of resonators, in some embodiments. That is,there can be, for example, 32 discrete channels used in the recordingdevice but only a 12-sided playback device, a 15-sided playback deviceor the like. These plurality of piezo-drivers are each attached to asingle sound reproduction device which amplifies sound waves emanatingfrom said plurality of piezo-drivers in some embodiments.

The above is described with reference to a single monaural recording ata single location using a single microphone. This can also be carriedout using two sets of devices as described above. This is akin to usingone recording device and one playback device for each ear, or what isknown in the art as recording and playback of stereo sound. Thus, insuch an embodiment, one would use two microphones, sound reflected orrefracted off a plurality of resonators each of the pluralitycorresponding to one of the two microphones (and placed in front of arespective microphone in the circular arrangement). For each of the twomicrophones, after applying a digital compression scheme (such as thetwist algorithm known in the art) to the output therefrom, the data isstored and playback proceeds (at the same time or a later time, uponretrieval of the stored data) as described in the above embodiment. Now,each playback device can be placed closer to a respective ear of aperson forming left and right audio, each producing holographic soundfor each left and right audio.

In the above embodiment, each microphone can be monaural andomni-directional and calibrated to receive sound substantially equallyfrom each resonator of a specific plurality of resonators correspondingto a respective one of the two microphones. So too, in the playbackdevice, there are a first set of piezo-drivers equi-spaced from a centerpoint and a second set of piezo-drivers equi-spaced from a second centerpoint on the sound reproduction device in some such embodiments. Eachfirst set and second set outputs recreate sound from a different one ofthe two microphones.

Said another way, a plurality of resonators, each of which resonates ata different frequency, are arranged in a substantially circulararrangement. A microphone is situated between the plurality ofresonators on at least one plane of a three dimension plane. A tangiblestorage medium stores a digital and compressed version of output fromthe microphone. A plurality of piezo-drivers arranged equi-distant froma center point on a sound reproduction device play back an uncompressedversion of the output from the microphone with output to specificpiezo-drivers of the plurality of piezo-drivers based on a determinedphase shift of at least some frequencies within the output of the sound(or input of the sound, recorded sound, and the like).

A directionality of sound recorded by said microphone is reproduced bythe piezo-drivers which cause vibrations through acoustic metamateriallayers attached to the sound reproduction device. An additional andsubstantially identical set of a plurality of resonators, themicrophone, and the plurality of piezo-drivers can be used to createsound together with the first set to produce binaural and/or stereosound. Playback by the plurality of piezo-drivers and additionalplurality of piezo-drivers allows for detection of a position of soundpicked up by the microphone and the additional microphone to be aurallydetermined in three-dimensional space relative to the plurality ofpiezo-drivers and the additional piezo-drivers.

The plurality of piezo-drivers are each attached to a single soundreproduction device which amplifies sound of the piezo-drivers inembodiments of the disclosed technology. Spacing of the piezo-drivers(relative to each other) has no correspondence with spacing of theplurality of resonators/discrete channels (relative to each other) inembodiments of the disclosed technology. The plurality of resonators arepseudo-randomly arranged in the substantially circular arrangement inembodiments of the disclosed technology. The plurality of resonators arebifurcated by a plurality of equi-spaced non-resonant material arrangedwithin the circular arrangement in embodiments of the disclosedtechnology. Each or the sole microphone used is monaural and the storagemedium stores sound received therefrom in a single channel of data,compressed, in embodiments of the disclosed technology.

“Substantially” and “substantially shown,” for purposes of thisspecification, are defined as “at least 90%,” or as otherwise indicated.Any device may “comprise” or “consist of” the devices mentionedthere-in, as limited by the claims.

It should be understood that the use of “and/or” is defined inclusivelysuch that the term “a and/or b” should be read to include the sets: “aand b,” “a or b,” “a,” “b.”

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a perspective view of a monaural recording device used inembodiments of the disclosed technology.

FIG. 2 shows a plan view of a monaural recording device used inembodiments of the disclosed technology.

FIG. 3 shows a high level diagram of a sound acquisition or recordingdevice used in embodiments of the disclosed technology.

FIG. 4 shows a cross section of the sound acquisition or recordingdevice of FIG. 3 turned 90 degrees relative to FIG. 3.

FIG. 5 shows a playback device used to exhibit holographic soundrecorded using embodiments of the disclosed technology.

FIG. 6 shows a first schematic representation of a recording device ofembodiments of the disclosed technology.

FIG. 7 shows a second schematic representation of a recording device ofembodiments of the disclosed technology.

FIG. 8 shows a high level flow chart of steps taking to carry outmethods of the disclosed technology.

FIG. 9 shows a high level block diagram of measuring and reconstructingholographic waves.

FIG. 10 is a high level block diagram showing devices on whichembodiments of the disclosed technology may be carried out.

DETAILED DESCRIPTION OF EMBODIMENTS OF THE DISCLOSED TECHNOLOGY

Holographic sound is recorded and reproduced by way of a single monauralrecording per left and right ear recorded. This is accomplished bydetermining the phase shift of frequencies recorded after dividing thesound into discrete frequencies in a recording device having resonators,each resonating at a different frequency, placed in a circulararrangement and divided into discrete channels by non-resonant material.The resonators are placed in a pseudo-randomized arrangement within therecording device and the circle of resonators is in front of amicrophone which records the sound monaurally. To achieve stereorecording, two such circular arrangements of resonators each associatedwith a single monaural microphone are used. Playback is then by way ofarranging speakers or transducers into micro perforated sheets whichamplify the sound, the arrangement of speakers/transducers around acentral point. The sound is then played back directionally based on theposition where the sound originally was recorded from and the positionof the particular transducer around the central point.

To understand embodiments of the disclosed technology, it is necessaryto explain the discoveries about the human ear and recording which havebeen made by the inventor.

The human ear cochlea can be viewed as a chain of globally forcedcoupled oscillators, and this model incorporates fundamental aspects ofboth the resonance and traveling wave theories. The spectrum-analysisarchitecture used by the biological cochlea is extremely efficient:analysis time, power and hardware usage all scale linearly with, thenumber of output frequency bins, versus N log(N) for the Fast FourierTransform. A graded bank of uncoupled harmonic oscillators withcochlear-like frequencies and quality factors is simultaneously excited,and that resonances gives rise to similar frequency responses, groupdelays, and traveling wave velocities as observed by experiment. A toneproduces global, near-simultaneous forcing in a graded bank of coupledresonators and this causes an apparent traveling wave. The band-passfilter mechanism is simulated by a bank of randomized Helmholtzresonators or subwavelength resonators in the present patent.

Acoustic meta materials (AMM) (defined as “a device used to absorb soundand reduce sound intensity comprised of, or consisting of, a thin flatplate less than, or equal to, 2 mm thick, with at least one hole or aseries of spaced-apart holes.”) combine geometrically placed spacing andresonance effects. For example, a conventional base material is modifiedso as to have a regular structure containing holes, channels, resonatorsor scattering sites leading to a material exhibiting negative effectivedensity (ρ_(eff)) and bulk modulus (K_(eff)), whereas normally they areboth positive, resulting in a negative acoustic refractive index((η_(eff)<0). A simple AMM resonator is Helmholtz resonator usedextensively in various applications. Helmholtz resonator, a well knownacoustic resonator, which is small compared to the wavelength whilepresenting relatively low losses due to viscous damping. The latterconsists of a rigid container embedding a volume V, terminated by anopen-ended neck of length l and cross section S. An acousticallyreflecting surface can be designed to acquire hybrid resonances whichbecomes impedance-matched to airborne sound at tunable frequencies, suchthat no reflection is generated. The Helmholtz resonator shown here isused as a baseline conventional element to explain the AMM concept. Whencompared to a single resonator, a duct with several identical resonatorsexhibits a unique attenuation characteristic caused by structuralperiodicity, and may, if carefully designed, provide a much broadernoise attenuation bands. This behavior of multiple resonators alludes toBloch (i.e., Bragg) wave phenomena which is also known as phononiccrystal behavior. It may be mentioned that phononic crystals are asub-class of acoustic meta-materials. A Helmholtz resonator used asacoustic resonator or scatterer can be tuned to a single designfrequencies with side band gaps introduced due to Bloch waves.

Since the resonant frequency of a unit depends only on its inertia (forexample, the mass) and the restoring force (for example, that of thespring), the relevant wavelength at the resonant frequency can be ordersof magnitude larger than the physical dimension of the resonant unit.This sub-wavelength characteristic is therefore a common feature of alltypes of meta materials, which also includes sub-wavelength structureswith functionalities not found in nature. The meta material propertiesare independent of the material used and are dependent only on thegeometry of the structure and the medium that fills it. Therefore thesestructures are ideal for the realization of tunable negative bulkmodulus. Sub-wavelength control of acoustic waves has not been studiedas much as in electromagnetic, but there have been few attempts in orderto realize super-resolution imaging based on canalization or hyperlens.

Compressed sensing (also known as compressive sensing, compressivesampling, or sparse sampling) is a signal processing technique forefficient acquisition and reconstruction of a signal, by findingsolutions to underdetermined linear systems. This is based on theprinciple that, through optimization, the sparsity of a signal can beexploited to recover it from far fewer samples than required by theShannon-Nyquist sampling theorem. There are two conditions under whichrecovery is possible. The first one is sparsity which requires thesignal to be sparse in some domain. The second one is incoherence whichis applied through the isometric property which is sufficient for sparsesignals. Compressed sensing is advantageous whenever signals are sparsein a known basis; measurements (or computation at the sensor end) areexpensive; but computations at the receiver end are cheap. Being able torecover images from incomplete data is very important: less time spenton imaging or other sensing technologies, relieves storage requirement,because only incomplete data is needed to recover all that we need andconserves energy. The signal of interest is sampled by taking smallnumber of linear random projections of the signal which contain most ofthe vital information about the signal. It basically relies on two majorassumptions about the signal i.e. sparsity and incoherence. Sparsitydepends upon the signal of interest and incoherence depends upon thesensing modality. Sparsity means that the amount of information presentin the signal is much less than the total bandwidth acquired by thesignal. Most of the natural signals are sparse in nature. On the otherhand, incoherence means that, signals that can be represented sparselyshould be spread out in the domain in which they are acquired. It isinteresting to note that sparsity lives in audio signals, radar,statistical models, PDE solutions and much more.

Acoustic meta materials are artificially fabricated materials designedto control, direct, and manipulate sound waves. Since the acoustic metamaterials are one of the branch of the meta materials, the basicprinciple of the acoustic meta materials is similar to the principle ofmeta materials. These meta materials usually gain their properties fromstructure rather than composition, using the inclusion of smallinhomogeneities to enact effective macroscopic behavior. Control of thevarious forms of sound waves is mostly accomplished through the bulkmodulus K_(eff) mass density ρ_(eff), and chirality. Acoustic metamaterials can be generally divided into two main areas. Resonantmaterials usually consist of a matrix material in which is embeddedperiodic arrangements of inhomogeneities such as resonators, rigidspheres or cylinders with spacing less than a wave-length. The embeddedstructures cause wave scattering and resonant behavior which createsstop bands and refraction effects. Non-resonant acoustic meta materialsare designed to control the propagation of acoustic waves through fluidsand materials. Both resonant and non-resonant meta material designs areused in the present patent. An acoustically reflecting surface canacquire hybrid resonances and becomes impedance-matched to airbornesound at tunable frequencies, such that no reflection is generated. Eachresonant cell of the meta surface is deep-subwavelength in all itsspatial dimensions, with its thickness less than the peak absorptionwavelength by two orders of magnitude. As there can be no transmission,the impedance-matched acoustic wave is hence either completely absorbedat one or multiple frequencies, or converted into other form(s) ofenergy, such as an electrical current.

Acoustic signals, such as, speech, music, etc. are information richsignals which has become the primary means of communication amonghumans. Digitizing real world signals helps to achieve more compactrepresentations and provides better utilization of available resources.Also, inverse problems abound in many application areas of signal/imageprocessing: remote sensing, radar imaging, tomographic imaging,microscopic imaging, astronomic imaging, digital photography, etc. Imagerestoration is one of the earliest and most classical linear inverseproblems in imaging, dating back to the 1960s. Signal processing theorystates that the rate at which signals must be sampled in order tocapture all of the information of that signal is equal to twice theFourier bandwidth of the signal (Nyquist rate). This sampling methodproduces a large amount of data with a large amount of redundantinformation. Traditionally, to recover a signal, enough samples need tobe taken to avoid aliasing and reconstruct with good accuracy. TheNyquist-Shannon sampling theorem states that to restore a signal exactlyand uniquely, you need to have sampled the signal with at least twiceits frequency, Of course, this theorem is still valid; if you skip onebyte in a signal or image of white noise, you can't restore theoriginal. But most interesting signals and images are not white noise.When represented in terms of appropriate, basis functions, such astrigonometric functions or wavelets, many signals have relatively fewnon-zero coefficients. In compressed (or compressive) sensingterminology, they are sparse. Shannon's theorem (also called theShannon-Nyquist sampling theorem) then says that the resolution of animage is proportional to the number of measurements. If you want todouble the resolution, number of pixels needs to be doubled.

With compressive sensing, the Nyquist criteria can be violated, as longas certain conditions such as signal sparsity and incoherence can beused to compensate for the limited measurements and, thus, still recoverthe signal accurately. It has been observed that many important signalshave this property of sparseness, thus allowing the number of samplesrequired to capture all of the signal's information to be reduced. Asignal is called sparse in nature if it has only a few significant(large in magnitude) components and a greater number of insignificant(close to zero) components.

In compressive sensing or sampling (CS) signal sparseness allows signalsto be under sampled without the loss of information. CS is defined as asignal processing technique for efficiently acquiring and reconstructinga signal, by finding solutions to under-determined linear systems. Thisis based on the principle that, through optimization, the sparsity of asignal can be exploited to recover it from far fewer samples thanrequired by the Shannon-Nyquist sampling theorem. There are twoconditions under which recovery is possible. The first one is sparsitywhich requires the signal to be sparse in some domain. The second one isincoherence which is applied through the isometric property which issufficient for sparse signals. In the compressed-sensing view of theworld, the achievable resolution is controlled primarily by theinformation content of the image. A signal is said to be compressible ifit is sparse in nature. An image with low information content can bereconstructed perfectly from a small number of measurements. Once therequisite number of measurements have been made, it doesn't help to addmore.

Compressive sensing is a technique in signal processing that allows foraccurate reconstruction of sparse signals given a limited number ofmeasurements and an under-determined linear system. However compressivesensing shows that this rule does not need to hold if we know that thesignal is sparse, and the system is incoherent, which means that thesystem should be able to spread out the sparse signal in themeasurement. When the system is coherent, or fails to spread out theoriginal signal appropriately, this technique fails. Since sparsity isthe main principle behind CS, effective sparse representations ofsignals play a major role in the success of CS based applications.Compressed sensing (CS) technology, for example, has recently shown thattomographic images can be well retrieved from far less sample data thanthe Shannon-Nyquist criterion.

“Ground truth” involves the collection of measurements and observationsabout the type, size, condition and any other physical or spectralproperties believed to be of importance concerning the acoustic sourcesand frequency content that are being sensed. CS comprises a collectionof methods of representing a signal on the basis of a limited number ofmeasurements and then recovering the signal from these measurements.

The signal to be acquired may be represented as follows:

s=ψx,

where s is signal to be acquired, ψ is sparsifying matrix and x is realvalued column vector.

$\begin{matrix}{{y = {\Phi_{s} = {{\Psi\Phi}\; x}}},} \\{= {{Ax} = {A_{k} \cdot \chi_{k}}}}\end{matrix}$

where y is compressed samples and ϕ is sensing matrix.The solution to above equation is:

X k = ( A k T  A k - 1  A k T  y

Above is an under-determined problem i.e. projection of an n-dimensionalvector into an M dimensional space i.e. Number of equations<Number ofUnknowns.

To solve this kind of problems, the concept of Norms is used. Normsassign strictly positive length to vectors in a vector space. Norms areof following types:

a. L0 Norm: It simply counts the number of non-zero components in avector

b. L1 Norm: It is given by the following equation:

${x}_{i} = {\sum\limits_{i = 1}^{N}{x_{i}}}$

L₂ Norm: It is given by following equation:

${x}_{2} = \left( {\sum\limits_{i = 1}^{N}{x_{i}}^{2}} \right)^{\frac{1}{2}}$

The resonant behavior of a Helmholtz resonator is due to the oscillationof the mass of the gas column located in the neck, while the cavitybehaves as the restoring force of the harmonic oscillator. The resonantfrequency of the Helmholtz resonator may therefore be simply written as:

$f = {\frac{c}{2\pi}\sqrt{\frac{S}{VI}}}$

The resonance frequency can occur in the low frequency range where theoperating wavelength is much larger than the resonator dimension. Byselecting the resonance frequencies properly, it is possible tosimultaneously achieve negative density and negative compressibilityover a finite range of frequencies. A system of independent resonatorscan produce traveling wave with zero transfer of energy in the directionof the travel.

In Helmholtz resonators, the effective bulk modulus, rather than theeffective mass density, becomes frequency-dependent. Theresonance-induced anomalous effective bulk modulus K_(eff) can beachieved by a waveguide shunted by a chain of Helmholtz resonators.Helmholtz resonance is characterized by the oscillation of the fluid inthe neck section under the restoring force provided by the compressionand expansion of the fluid in the cavity. The sample is sub-wavelengthin its dimension. Negative bulk modulus, caused by the frequencydispersion of the local resonances, is obtained. The hidden source for aHelmholtz-resonator-based meta material is the extra air volume injectedfrom the resonator cavity. An AMM meta surface with sub-wavelength scaleunit cells that is impedance-matched to airborne sound at tunablefrequencies is achieved by coupling different resonators and generatinga hybrid resonance mode.

Designing a Sensing Matrix: Following conditions need to be strictlysatisfied while designing a sensing matrix so that, the signal isrecovered faithfully:

Universal Incoherence condition: The value of cross correlation betweentwo channels or column vectors of a sensing matrix must be minimum.

Data Independence: The construction of a random matrix does not dependupon any prior knowledge of data.

Robustness: Transmission of randomly projected coefficients is robust topacket loss in the network.

Incoherence condition: The sensing matrix should be as different fromthe sparsifying matrix. Time and frequency basis are maximallyincoherent. Following equation signifies the incoherence condition:

μ<1/(2K−1)

Embodiments of the disclosed technology will become clearer in view ofthe following description of the figures.

Referring first to FIGS. 1-3, these figures show a sound acquisitionsystem using acoustic meta material layers forming resonators andnon-acoustic separation barriers separating groups of resonators intodiscrete channels. The exterior shape of the sound acquisition devicecan be spherical, conical, or formed from a regular polygon extended inthree dimensional space. The distances given (non-bold numbers) in FIGS.1 and 2 are in millimeters showing the size of the sound recording oracquisition system in a particular embodiment. It should be understoodthat the size can vary and the sizes given are for exemplary purposesonly.

Referring first to FIGS. 3 and 4, FIG. 3 shows a high level diagram of asound acquisition or recording device used in embodiments of thedisclosed technology. FIG. 4 shows a cross section of the soundacquisition or recording device of FIG. 3 turned 90 degrees relative toFIG. 3. Two such devices 300 each form one monaural recording device,such as for left and right sides. Each comprises a plurality of acousticresonators 310, each resonator resonating at specific discretefrequencies and surrounding a (monaural and omni-directional, in someembodiments) microphone 390. The left half of the system records soundfor the left recording/sound representing a left ear and the right halffor the right recording/sound (i.e., right ear). The distance d1 betweenthe centers of two recording devices 300 can be set to binaural orstereo recording requirements. The distance d1 for binaural can be thedistance between the ears the intended listened (about 21.5 cm). Thedistance d1 for stereo recording and playback via two playback devicescan be between about 1 meters and 25 meters, by way of example. Each AMMrecording system has several channels, defined by the resonators 210placed between each layer of non-resonant material 315. Each channelcomprises resonators with randomized resonances and a recordingmicrophone at the center of the system. After the sound is received bythe microphone 390, it is sent to, in some embodiments, apre-amplification device 410 which amplifies the sound and then a dataacquisition system 520 which manipulates the data and stores the data toa tangible storage medium.

Embodiments of the disclosed technology will become more clear in viewof the following discussion of the figures.

FIG. 1 shows a perspective view of a monaural recording device used inembodiments of the disclosed technology. As described above, inembodiments two such monaural recording devices 300 are used. Eachdevice 300 has a plurality of Helmholtz/acoustic sub-wavelengthresonators of varying volumes (relative sizes to each other). Some arelarger and some are smaller in order to vary at different frequencies,each. The resonators 310 are placed randomly or pseudo-randomly inposition around a center point of the device 300 to provide maximumresonant dispersion. A face plate over the resonators has a specificpercent open area (POA), thickness and hole diameter which covers theresonators in each sound acquisition device 300 to provide acousticimpedance matching for incoming acoustic signals. Similar randomizeddispersion in resonator channels can also be achieved by varying holediameter and keeping the volume (size) of resonators constant, as betterdescribed when viewing FIG. 2.

FIG. 2 shows a plan view of a monaural recording device used inembodiments of the disclosed technology. The resonating dispersion ofeach channel (resonators between non-resonant layers 315 whichacoustically separate a group of resonators 310 from one another intothe discrete channels) has a plurality of Helmholtz (acoustic)resonators distributed into channels separated by layers 315. Theresonances are randomized or pseudo-randomized and contribute to ameasurement matrix that supports compressive sensing, as describedabove. The randomized modulation from all of the channels “scrambles”the original omni-directional measurement modes of the single sensorwhich an omni-directional microphone 390 in embodiments of the disclosedtechnology, placed in the center of a ring of resonators 310 andchannels. As a result, the measurement modes are complex in both thespatial and spectral dimensions.

Skipping now to FIG. 9, FIG. 9 shows a high level block diagram ofmeasuring and reconstructing holographic waves. Assuming the resonancesin each channel (the group of resonators 310 between each non-resonantsection 315) are distributed sparsely over the frequency range ofinterest and only first-order filtering responses dominate, the overallfrequency modulation of a waveguide can be approximated by themultiplication of the individual responses of the resonators:

T _(i)(ω)=π_(j) T _(ij)(ω)

For a source located at r_(k)′, frequency response can be derived bypropagating the waveguide responses from each waveguide aperture ŕ_(i)to the source location ŕ_(k):

${G\left( {\omega,{\overset{\rightarrow}{r}}_{i},{\overset{\rightarrow}{r}}_{k}} \right)}{T_{i}(\omega)}{R\left( {\omega,{\overset{\rightarrow}{r}}_{i},{\overset{\rightarrow}{r}}_{k}} \right)}$${P_{c}\left( {\omega,{\overset{\rightarrow}{r}}_{k},S_{0}} \right)} = {{a(\omega)}{S_{0}(\omega)}{\sum\limits_{i = 1}^{N}}}$

where S₀(ω) is the spectrum of the audio signal from the source,R(ω,{right arrow over (r)}_(i),{right arrow over (r)}_(k)) is the AMMchannel radiation pattern which is mostly determined by the shape of thechannel, aperture, and

$G\left( {\omega,{\overset{\rightarrow}{r}}_{i},{{\overset{\rightarrow}{r}}_{k} = \begin{matrix}{{\overset{\rightarrow}{r}}_{i},{- {\overset{\rightarrow}{r}}_{k}}} \\{{\overset{\rightarrow}{r}}_{i},{- {\overset{\rightarrow}{r}}_{k}}} \\{e^{- {jk}}{/}}\end{matrix}}} \right.$

is the Green's function from the location ŕ_(i) of the aperture of thei^(th) channel to the location ŕ_(k). The coefficient α(ω) includes allother factors such as sensor and speaker responses that are uniform fordifferent source locations and audio signals.

Each column of the measurement matrix

$H = \begin{bmatrix}{h_{11}h_{12}} & \ldots & h_{1N} \\⋰ & \ddots & ⋰ \\{h_{M\; 1}h_{M\; 2}} & \ldots & h_{MN}\end{bmatrix}$

represents the discretized Fourier components of source emitting themusic signal from one of the speakers on the recording stage. The numberof columns of the matrix is N=K×P, where K is the possible speakerlocations on the stage and P is the size of the audio segments.

Each row H_(mn) of the measurement matrix (i.e., H) represents a testfunction for the object vector at one frequency, because a measurementvalue in the measurement data vector is sampled in the way defined bythe test function as g_(m)=f,H_(m)>, where the angle bracket denotes theinner product. The randomization of the measurement matrix for the AMMacoustic sensing system is contributed by the carefully designed AMMchannel responses T_(i)(ω).

An element in the measurement matrix may be expressed as:

${G\left( {\omega_{m},{\overset{\rightarrow}{r}}_{i},{\overset{\rightarrow}{r}}_{k}} \right)}{T_{i}\left( \omega_{m} \right)}{R\left( {\omega_{m},{\overset{\rightarrow}{r}}_{i},{\overset{\rightarrow}{r}}_{k}} \right)}$$h_{mn} = {{P_{c}\left( {\omega_{m},{\overset{\rightarrow}{r}}_{k},S_{p}} \right)} = {{a\left( \omega_{m} \right)}{S_{p}\left( \omega_{m} \right)}{\sum\limits_{i = 1}^{q}}}}$

Thus P_(c)(ω,{right arrow over (r)}_(k),S_(p)) represents frequencyspectra (amplitude and frequency content) of the sources, each atdifferent (ŕ_(k), location, and can be determined through h_(mn).

A problem now arises of how to effectively recover the original signalfrom the compressed data, an is solved by the present technology. Basispursuit (BP) is a popular mathematical optimization problem which isbased on constrained 11 norm minimization, and the split Bregman methodis an effective technique for solving a variety of L1-regularizedoptimization problems. Several reconstruction algorithms based onconstrained Lp norm minimization with p<1 have also been proposed.Furthermore, a signal reconstruction algorithm based on the optimizationof a smoothed approximate L0 norm (SL0) is studied in where simulationresults are compared with corresponding results obtained from severalexisting algorithms. The results favor the use of the approximate L0norm.

The Two-Step Iterative Shrinkage Thresholding (TwIST) is an algorithmthat provides solutions to inverse linear problems. The TwIST algorithmis known in the art and described, at the time is writing, for exampleat http://www.1x.it.pt/˜bioucas/TwIST/TwIST.htm which is quoted here infull:

Many approaches to linear inverse problems define a solution (e.g., arestored image) as a minimizer of the objective function where y is theobserved data, K is the (linear) direct operator, and F(x) is aregularizer. The intuitive meaning of f is simple: minimizing itcorresponds to looking for a compromise between the lack of fitness of acandidate estimate x to the observed data, which is measured by ∥y−Kx∥2,and its degree of undesirability, given by F(x). The so-calledregularization parameter 1 controls the relative weight of the twoterms.

State-of-the-art regularizers are non-quadratic and non-smooth; thetotal variation and the lp norm are two well known examples of suchregularizers with applications in many statistical inference andsignal/image processing problems, namely in deconvolution, MRIreconstruction, wavelet-based deconvolution, Basis Pursuit, LeastAbsolute Shrinkage and Selection Operator (LASSO), and CompressedSensing.

Iterative shrinkage/thresholding (IST) algorithms have been recentlyproposed to the minimization of f, with F(x) a non-quadratic, maybenon-smooth regularizers. It happens that the convergence rate of ISTalgorithms depends heavily on the linear observation operator, becomingvery slow when it is ill-conditioned or ill-posed. Two-step iterativeshrinkage/thresholding TwIST algorithms overcome this shortcoming byimplementing a nonlinear two-step (also known as “second order”)iterative version of IST. The resulting algorithms exhibit a much fasterconvergence rate than IST for ill conditioned and ill-posed problems.

An inverse problem in science is the process of calculating from a setof observations the causal factors that produced them. TwIST has beenused to solve many image restoration and compressed sensing problems.The recent approach for restoration of images is the use of wavelets ina two step process, the TwIST. The two steps, in TwIST are IterativeShrinkage and Thresholding. TwIST algorithm produces faster convergencecompared to conventional IST algorithms even for ill conditionedproblems.

The two-step iterative shrinkage-thresholding (TwIST) algorithm based ona second-order approach is used to improve convergence performance. Inan iterative optimization process based on a Fourier space, the TwISTalgorithm shows a convergence rate better than that of other first-ordermethods. When compared to other Iterative Shrinkage/Thresholding (IST)algorithms TwIST is more effective since its convergence is based onboth past and present iterations. The iterative shrinkage-thresholding(IST) algorithm is derived from a consideration of the L1-norm of theproximal gradient method and is now a common tool for image recovery—onethat is based on the principle of CS. A soft-thresholding filteringalgorithm using a pseudo-inverse of a discrete difference transformdemonstrates a good image recovery.

The TwIST algorithm can be used, in step 210, to handle highly ill posedde-noising problems. In an inverse problem, the goal is to estimate anunknown original signal/image x from a (possibly noisy) observation y,produced by an operator K applied to x. For the linear system ofill-conditioned problems

y=Kx

where, for different values of x the image is observed.

In TwIST, the approach is to solve the minimization problem:

f(x)=½∥y−Ax∥ ²+λφ(x),

where λ is a constant weight factor, N is the noise vector, y is themeasurement, and A is the system matrix, ϕ is a regularization function,and ½ is an energy matching coefficient.

Many approaches to linear inverse problems define a solution (e.g., arestored image) as a minimizer of the objective function

f(x)=½∥y−Kx∥ ²+λΦ(x),

where y is the observed data, K is the (linear) direct operator, andF(x) is a regularizer. The intuitive meaning of f is simple: minimizingit corresponds to looking for a compromise between the lack of fitnessof a candidate estimate x to the observed data, which is measured by∥y−Kx∥2, and its degree of undesirability, given by F(x). The so-calledregularization parameter 1 controls the relative weight of the twoterms. Two-step iterative shrinkage/thresholding TwIST algorithms byimplements a nonlinear two-step (also known as “second order”) iterativeversion of IST. The resulting algorithms exhibit a much fasterconvergence rate than IST for ill conditioned and ill-posed problems.

The TwIST method aims at keeping the good de-noising performance of theIST scheme, while still being able to handle ill-posed problems asefficiently as the IST algorithm. In this method a new class ofiterative methods, called TwIST, which have the form of Two-stepIterative Shrinkage/Thresholding (TwIST) algorithms has been used. Theupdate equation depends on the two previous estimates (thus, the termtwo-step), rather than only on the previous one. This class contains andextends the Iterative Shrinkage/Thresholding (IST) methods.

The sensing system of the present technology has randomized placement(or pseudo-randomized placement) of Helmholtz resonators with a generalsampling model as g=Hf, where g is the vector form of the measured data(measurement vector); f is the object vector to be estimated. Themeasurement matrix H, which represents the forward model of the sensingsystem, is formed by stacking rows of linear sampling vectors [alsoknown as test functions] at sequentially indexed frequencies. Thismatrix is randomized by the physical properties of the meta materials togenerate highly uncorrelated information channels for sound wave fromdifferent azimuths and ranges. The level of randomization of the matrixdetermines the supported resolution and the multiplexing capability ofthe sensing system.

Now referring to the A multi-speaker system provides acoustic signalsbeing played through several speakers on the stage. A Fourier componentof the collected signal can be expressed as the superposition of theresponses from all of the waveguides at this frequency:

F i  ( ω ) ${F_{c}(\omega)} = {\sum\limits_{i}^{N}}$

is the response from the i^(th) AMM channel.

The measured data vector to be used for reconstruction is

g = [ F c  ( ω 1 )  F c  ( ω 2 )   …   F c  ( ω M ) T ,

and the object vector f is a scalar vector containing N=K×P elements (Kis the number of the possible locations and P is the size of the finiteaudio library). Because of the sparsity of f (only several elements arenonzero, corresponding to the activated sources), the sensing process isan ideal fit for the framework of compressive sensing. L1-normregularization is performed with the Two-step IterativeShrinkage/Thresholding (TwIST) algorithm to solve the ill-posed inverseproblem.

In an inverse problem, the goal is to estimate an unknown originalsignal/image x from a possibly noisy observation y, produced by anoperator K applied to x. For the linear system of ill-conditionedproblems

y=Kx

Where, for different values of x the image is observed.

Now, in step 210 (still referring to FIG. 9), from the TwIST method forlinear system, a linear function Ax=B is considered where the matrix Ais split to C and R given below (in step 230):

A=C−R,

Taking C=I+λDt and R=I−KTK in the above equation (step 240)

A=λDt+KTK,

The two-step iteration for linear system Ax=B becomes (step 250)

Xt+1=(1−a)xt−1+(α−β)xt−1+(1−Υ)xt+βΓλ(xt)A=λDt+KTK,

The process of TwIST is performed (step 260):

X1=Γλ(x0)

Xt+1=(1−α)xt−1+(α−β)xt+βΓλ(xt)

The different values of α and β are set as follows (step 270):

α=ρ2+1,

β=2α/(ξm+ξ1)

where he value of p is given as (step 280):

=(1−√{square root over (k)})/(1+√{square root over (k)})<1

If convergence (step 290) is proved the iteration is stopped (step 295),otherwise the process is reiterative and steps 260-290 are carried outagain.

The non-resonant acoustic meta material (AMM) impedance system usingmicro-perforated panels (MPP) periodically arranged within porous layersand air gaps used in embodiments of the disclosed technology layereddevice are optimized for acoustic impedance in addition to soundabsorption. Traditional micro-perforates are tuned to certainfrequencies, as done for Helmholtz resonators, whereas in the presenttechnology, AMM devices are tuned over a frequency range of 20-20000 Hz.In embodiments of the disclosed technology, non-resonant acoustic metamaterial layers which utilizes periodic arrangement of meta material MPPsheets and sound absorptive layers as well as air gaps are used. Thethickness and material properties of absorptive layers and designparameters of micro-perforated sheets, such as hole diameter, holespacing etc., are optimized using the meta material approach [Ref]. TheAMM impedance matching is essentially frequency independent and may betailored by the geometry of the acoustic meta material speaker system.

Now discussing FIG. 5, FIG. 5 shows a playback device used to exhibitholographic sound recorded using embodiments of the disclosedtechnology. Relative size is shown in the non-bolded numerals, such a inmillimeters. In this high level drawing of a polyhedral speaker 500 (asshown, 10-sided) piezoelectric actuators 510 (a single one is shown, buteach section/side of the polyhedron has same in embodiments of thedisclosed technology) reproduce an acoustic hologram. Multiplepiezoelectric actuators may be bonded to the surfaces of the polyhedronspeaker. In another embodiment, multiple conventional loudspeakers canare used to reproduce an acoustic hologram. The speakers must bearranged in three dimensions around a center point, the center pointequivalent to the position of the microphone 390 used to record theholographic sound. The reproduction functions by way of exhibiting thesound at the direction (three dimensional vector in space relative tothe recording point) from the center point from where the soundemanated. In this manner, the sound is reproduced and exits, in theexample of the polyhedral speaker 500, in directions 1 and 2 transverseto the direction of sound propagation from the resonator plates 510. Theresonators 510 can be acoustic meta-materials vibrated by, andamplifying the sound from, piezoelectric transducers. One such soundplayback device 500 or set of speakers can be used for each recordedholographic sound, such as one for a left ear and one for a right ear.

FIG. 8 shows a high level flow chart of steps taking to carry outmethods of the disclosed technology. In step 110, acoustic resonatorsare arranged into discrete (individual and separated) channels in apseudo-random circular arrangement. A microphone, such as a monauralomni-directional microphone placed in front of or at the end of theacoustic resonators of the recording device and centered there-betweeneach of, a plurality of, some of, or most of the circular cross sectionsof the acoustic resonators of the recording device. Output sound fromtwo or more sources or points in three dimensional space (meaning,having different distances from the microphone in at least one, two, orthree distances on an X, Y, and Z coordinate plane) is created in step120. The output sound from the ambient space around the recording devicecauses the resonators to resonate. Each is tuned to a specific frequencysuch as at 1 Hz, 2 Hz, 5 Hz, or 20 Hz difference from another, butpseduo-randomly arranged within the circular arrangement and/or withinthe discreet channels. This sound is then picked up by the microphoneafter being reflected off of the resonators in addition to being pickedup by the microphone directly without the reflection, in someembodiments. Based on the time difference between the sound hitting themicrophone directly and being reflected off of the resonator for aparticular frequency, and knowing how far the resonator is from themicrophone, one can calculate, as above, the direction of the source ofthe sound, at least partially. By combining this with the myriad ofother frequencies, latency, and position of the resonator for theparticular sound, one then calculates, in step 340 the phase shift ofthe sound waves to enough of a degree to determine the position of eachsound relative to the microphone.

The received sound into the microphone is then compressed and stored ina single channel (monaural sound recording) of output from the circulararrangement (recording device) in step 160. Two recording devices can beused in order to create a stereo recording, and as such, one monauralchannel is created from each recording device. The recording devices arethen, in this embodiment, duplicative such that there are two circulararrangements with discrete channels and with their own monauralmicrophone, the output of which are each recording into a singlemonaural recording (step 160). Together, this forms a stereo recording.

Steps 170 and 180 are the steps taken for playback. Playback can be inreal-time (as soon as allowed by the processors, networked devices, andtransmission devices between the recording device and playback device)or at a later time from the recording. To do so, in step 170,piezo-drivers or speakers are arranged equidistant or substantiallyequidistant from a center point for each channel. Sound is then playedback through specific piezo-drivers, in step 180, based on thepreviously determined phase shift as stored within each or the solemonaural channel.

Referring back to FIGS. 6 and 7, schematic representations of recordingdevices of embodiments of the disclosed technology are shown. FIG. 6shows a first schematic representation of a recording device ofembodiments of the disclosed technology. FIG. 7 shows a second schematicrepresentation of a recording device of embodiments of the disclosedtechnology. The top of the page has lower frequencies while the bottomof the page has higher frequencies. As this is a section/wedge of thecircle (see FIG. 1), one is looking at a cross-section of the circlewith lower frequencies requiring larger resonators, while higherfrequencies require smaller resonators and are typically more towardsthe outside of the circle. Each insulative layer 315 on the outer sideand a face plate 319, having a plurality of holes 317 through whichsound passes in to the sub-wavelength resonators on the inner side ofthe recording device in embodiments of the disclosed technology. Flipped90 degrees, one can see the depth of the resonators 310 in the smallerfigures to the right and below the cross section.

FIG. 10 shows a high-level block diagram of a device that may be used tocarry out the disclosed technology. Device 600 comprises a processor 650that controls the overall operation of the computer by executing thedevice's program instructions which define such operation. The device'sprogram instructions may be stored in a storage device 620 (e.g.,magnetic disk, database) and loaded into memory 630, when execution ofthe console's program instructions is desired. Thus, the device'soperation will be defined by the device's program instructions stored inmemory 630 and/or storage 620, and the console will be controlled byprocessor 650 executing the console's program instructions. A device 600also includes one, or a plurality of, input network interfaces forcommunicating with other devices via a network (e.g., the Internet). Thedevice 600 further includes an electrical input interface. A device 600also includes one or more output network interfaces 610 forcommunicating with other devices. Device 600 also includes input/output640, representing devices which allow for user interaction with acomputer (e.g., display, keyboard, mouse, speakers, buttons, etc.). Oneskilled in the art will recognize that an implementation of an actualdevice will contain other components as well, and that FIG. 4 is a highlevel representation of some of the components of such a device, forillustrative purposes. It should also be understood by one skilled inthe art that the method and devices depicted in FIGS. 1 through 9 may beimplemented on a device such as is shown in FIG. 10.

Further, it should be understood that all subject matter disclosedherein is directed, and should be read, only on statutory, non-abstractsubject matter. All terminology should be read to include only theportions of the definitions which may be claimed. By way of example,“computer readable storage medium” is understood to be defined as onlynon-transitory storage media.

While the disclosed technology has been taught with specific referenceto the above embodiments, a person having ordinary skill in the art willrecognize that changes can be made in form and detail without departingfrom the spirit and the scope of the disclosed technology. The describedembodiments are to be considered in all respects only as illustrativeand not restrictive. All changes that come within the meaning and rangeof equivalency of the claims are to be embraced within their scope.Combinations of any of the methods and apparatuses described hereinaboveare also contemplated and within the scope of the invention.

1-10. (canceled)
 11. A device for receiving and reproducing sound inthree dimensions, comprising: a plurality of resonators, each whichresonates at a different frequency, arranged in a substantially circulararrangement; a microphone situated between said plurality of resonatorson at least one plane of a three dimension plane; a tangible storagemedium storing a digital version of said sound after applying compressedsensing to output from said microphone; a plurality of flat-surfacedpiezo-drivers arranged equi-distant from a center point on a soundreproduction device having at least eight equal sides, playing back anuncompressed version of said output from said microphone with output tospecific piezo-drivers of said plurality of piezo-drivers based on adetermined phase shift of at least some frequencies within said outputand an orientation of said specific piezo-driver of said pluralitythereof.
 12. The device of claim 11, wherein a directionality of soundrecorded by said microphone is reproduced by said piezo-drivers whichcause vibrations through acoustic meta material layers attached to saidsound reproduction device.
 13. The device of claim 11, comprising anadditional and substantially identical set of said plurality ofresonators, said microphone, and said plurality of piezo-drivers suchthat output from said microphone and an additional said microphonerecords sound in binaural or stereo and playback by said plurality ofpiezo-drivers and additional said plurality of piezo-drivers allows fordetection of a position of sound picked up by said microphone and saidadditional said microphone to be aurally determined in three-dimensionalspace relative to said plurality of piezo-drivers and said additionalpiezo-drivers.
 14. The device of claim 11, wherein said plurality ofpiezo-drivers are each attached to a single said sound reproductiondevice which amplifies sound of said piezo-drivers.
 15. The device ofclaim 14, wherein spacing of said piezo-drivers has no correspondencewith spacing of said plurality of resonators.
 16. The device of claim11, wherein said plurality of resonators are pseudo-randomly arranged insaid substantially circular arrangement.
 17. The device of claim 16,wherein said plurality of resonators are bifurcated by a plurality ofequi-spaced non-resonant material arranged within said circulararrangement.
 18. The device of claim 11, wherein said microphone ismonaural and said storage medium stores sound received therefrom in asingle channel of data in said compressed version.